Without a specific topic, this question has almost limitless answers. What part of the story do you want to focus on, and from which academic perspective? It is possible to analyze Heart of Darkness from many perspectives, including historical, social, literary, scientific....
Nevertheless, some common tips can be useful. First, know how your chosen perspective affects your understanding of the book. For example, if you are writing from a medical viewpoint, you might write: "While Kurtz chose his actions based on his ideals of power, he was also affected by sickness, causing him to overcompensate for what he felt as a personal weakness." This allows an analysis of Kurtz's character from both the literal -- his actions -- and the inferred -- his medical condition, which likely affected his thinking.
Similarly, if you were to focus on a historical aspect, you might write: "The brutal treatment of the natives by the whites is explicitly repeated when they attack Marlow's riverboat." Again, the literal event of the attack is contrasted with the inferred "revenge" that Marlow fears, which are supported by the brutality of European colonization in Africa.
Regardless of your chosen perspective, you should focus on at least two areas: literal and inferred. This allows the analysis of the text without simply reiterating the story point-by-point; many perspectives can be used to contrast the novel with reality. You might even choose a more literal approach and contrast the film Apocalypse Now with the original novel, examining how the story changed between writer and adaptation; this allows a literal approach combined with the socio-political motivations of the anti-Vietnam War movement.
Your thesis statement will drive your entire essay, and to write a meaningful paper, your thesis should be a statement which reflect something you truly believe. What is your reaction to this novel? What strikes you as most significant? What aspect can you research further? What literary elements did the author employ that you can examine and discuss in a relevant, impactful way? Do you discuss the darkness itself? The madness? The idea of dashed expectations? Colonialism?
Without more information about your specific assignment, it would be difficult to assist you further.